Question

The Social Security Administration determined that an average 30-year-old male in 2018 could expect to live at least 52.2 more years and that an average 30-year-old female in 2018 could expect to live at least 55.8 more years. (a) To what age could an average 30 -year-old male expect to live? Express your answer as an inequality. (b) To what age could an average 30 -year-old female expect to live? Express your answer as an inequality. (c) Who can expect to live longer, a male or a female? By how many years?

Short answer

(a) x ≥ 82.2(b) x ≥ 85.8(c) Female by 3.6 years

Step-by-step solution

Determine Expected Age for Males

The average 30-year-old male can expect to live at least 52.2 more years. Add this to the current age of 30 years: 30 + 52.2 = 82.2 Thus, the inequality for the expected age of a male is: x ≥ 82.2

Determine Expected Age for Females

The average 30-year-old female can expect to live at least 55.8 more years. Add this to the current age of 30 years: 30 + 55.8 = 85.8 Thus, the inequality for the expected age of a female is: x ≥ 85.8

Compare Ages

From Step 1, an average 30-year-old male can expect to live to at least 82.2 years. From Step 2, an average 30-year-old female can expect to live to at least 85.8 years. To determine who can expect to live longer and by how many years: 85.8 - 82.2 = 3.6 Therefore, an average 30-year-old female can expect to live 3.6 years longer than a 30-year-old male.

Key concepts

Life Expectancy

Life expectancy refers to the average number of years an individual is expected to live, based on statistical averages. It is influenced by various factors including genetics, lifestyle, healthcare quality, and socio-economic status. In our exercise, the Social Security Administration provided that a 30-year-old male in 2018 could expect to live at least 52.2 more years, making his expected age 82.2 years. Similarly, a 30-year-old female could expect to live at least 55.8 more years, or until 85.8 years. Understanding these averages helps in planning for the future, such as retirement and healthcare needs.

Inequality

Inequality in life expectancy means there are differences in the average number of years people live, typically influenced by factors like gender, race, economic status, and geography. In this exercise, we see a clear gender-based inequality. The inequality expressions would be: for males, the expected age is at least 82.2 years ( x ≥ 82.2). For females, the expected age is at least 85.8 years ( x ≥ 85.8). Recognizing such inequalities is crucial for policymakers to address health disparities and improve overall life expectancy.

Age Comparison

Age comparison helps us understand differences in life expectancy between different groups. Our exercise compares the expected ages of 30-year-old males and females. By calculating, we find that females are expected to live longer than males by 3.6 years. This is determined by subtracting the male life expectancy from the female life expectancy: 85.8 years - 82.2 years = 3.6 years. These comparisons can highlight the need for targeted health interventions aimed at those with shorter life expectancies.

Gender Differences

Gender differences in life expectancy often show that females live longer than males. The reasons for this trend can be complex, involving biological, social, and behavioral factors. In our example, 30-year-old females are expected to live 3.6 years longer than their male counterparts. Biological factors might include differences in hormones and genetics. Social factors could involve risk behaviors and lifestyle choices that differ between genders. Understanding these differences can help develop strategies to improve life expectancy for all genders.